Boundary‐Element Analysis

This chapter discusses boundary-element (BE) methods for computing the radiated sound field of vibrating structures, including methods for coupling structural vibrations and acoustic fields together. It also discusses the formulation for coupled finite-element/BE computations. A thorough discussion of BE methods is then given, beginning from the Rayleigh integral and progressing to the Kirchhoff-Helmholtz integral equation, focusing primarily on user interaction with a BE program. A potential disadvantage of BE methods is the so-called nonuniqueness difficulty. The chapter explains the difficulty in mathematical terms. Impedance boundary conditions are commonly used to model porous sound insulation material in BE simulations. As solving the system of equations is time-consuming, especially when the number of acoustic degrees of freedom becomes large, various techniques, including interpolation in frequency, parallelization, remeshing and multipole expansions have been developed to reduce computation times and allow larger problems to be addressed.